SpringerLink
Log in

The gamma power half-logistic distribution: theory and applications

  • Original Article
  • Published:
São Paulo Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

In this paper, we propose a new three-parameter distribution defined on the positive real line, called the gamma power half-logistic distribution. It constitutes an extension of the power half-logistic distribution using the gamma generated mechanism. The capabilities of the parent distribution are thus improved in several aspects. In particular, the hazard rate function now presents increasing failure, decreasing failure, and bathtub shapes, which are demanded characteristics in the context of statistical modelling. Other features related to the quantiles, skewness, kurtosis, moments, incomplete moments, mean deviations, Bonferroni and Lorenz curves, stochastic ordering, reliability parameter, and distributions of order statistics are also discussed. Subsequently, the gamma power half-logistic model is investigated using real-world results. We use the classical maximum likelihood method for estimating the model parameters, with a simulation trial demonstrating the effectiveness of the method for large enough sample sizes. Then, four real-life data sets of different sizes are used for the concrete application of the model, demonstrating its superiority in fitting compared to similar models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Afify, A.Z., Altun, E., Alizadeh, M., Ozel, G., Hamedani, G.G.: The odd exponentiated half-logistic-G family: properties, characterizations and applications. Chil. J. Stat. 8(2), 65–91 (2017)

    MathSciNet  MATH  Google Scholar 

  2. Anwar, M., Bibi, A.: The half-logistic generalized Weibull distribution. J. Probab. Stat., Volume 2018, Article ID 8767826, 12 pages (2018)

  3. Balakrishnan, N.: Order statistics from the half logistic distribution. J. Stat. Comput. Simul. 20, 287–309 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  4. Balakrishnan, N.: Handbook of the Logistic Distribution, vol. 123 of Statistics: A Series of Textbooks and Monographs, Marcel Dekker, New York, USA (1992)

  5. Balakrishnan, N., Puthenpura, S.: Best linear unbiased estimators of location and scale parameters of the half logistic distribution. J. Stat. Comput. Simul. 25, 193–204 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  6. Casella, G., Berger, R.L.: Statistical Inference. Brooks/Cole Publishing Company, USA (1990)

    MATH  Google Scholar 

  7. Castellares, F., Santos, M.A.C., Montenegro, L., Cordeiro, G.M.: A gamma-generated logistic distribution: properties and inference. Am. J. Math. Manag. Sci. 34, 14–39 (2015)

    Google Scholar 

  8. Chen, G., Balakrishnan, N.: A general purpose approximate goodness-of-fit test. J. Qual. Technol. 27, 154–161 (1995)

    Article  Google Scholar 

  9. Cordeiro, G.M., Alizadeh, M., Marinho, P.R.D.: The type I half-logistic family of distributions. J. Stat. Comput. Simul. 86(4), 707–728 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  10. Cordeiro, G.M., Alizadeh, M., Ortega, E.M.M.: The exponentiated half logistic family of distributions: properties and applications. J. Probab. Stat., vol. 2014, Article ID 864396, 21 pages (2014)

  11. Cox, D.R., Hinkley, D.V.: Theoretical Statistics. Chapman and Hall, London (1974)

    Book  MATH  Google Scholar 

  12. David, H.A., Nagaraja, H.N.: Order Statistics. Wiley, New Jersey (2003)

    Book  MATH  Google Scholar 

  13. DiDonato, A.R., Morris, J.A.H.: Computation of the incomplete gamma functions. ACM Trans. Math. Software 12, 377–393 (1986)

    Article  MATH  Google Scholar 

  14. Doornik, J.A.: Ox 5: An Object-Oriented Matrix Programming Language, 5th edn. Timberlake Consultants, London (2007)

    Google Scholar 

  15. El-Sherpieny, E.S.A., Elsehetry, M.M.: Kumaraswamy type I half logistic family of distributions with applications. GU J. Sci. 32(1), 333–349 (2019)

    Google Scholar 

  16. Kenney, J., Kee**, E.: Mathematics of Statistics. Vol. 1, 3rd edition, Princeton: NJ, Van Nostrand (1962)

  17. Korkmaz, M.Ç., Chesneau, C., Korkmaz, Z.S.: On the arcsecant hyperbolic normal distribution. Properties, quantile regression modeling and applications. Symmetry 13, 1–24 (2021)

    Article  MATH  Google Scholar 

  18. Kotz, S., Lumelskii, Y., Pensky, M.: The Stress-Strength Model and its Generalizations and Applications. World Scientific, Singapore (2003)

    Book  MATH  Google Scholar 

  19. Krishnarani, S.D.: On a power transformation of half-logistic distribution. J. Probab. Stat. 20, 1–10 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  20. Lemonte, A.J.: A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function. Comput. Stat. Data Anal. 62, 149–170 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  21. Moors, J.J.A.: A quantile alternative for kurtosis. Statistician 37, 25–32 (1998)

    Article  Google Scholar 

  22. Nadarajah, S., Cordeiro, G.M., Ortega, E.M.M.: The Zografos-Balakrishnan-G family of distributions: mathematical properties and applications. Commun. Stat. Theory Methods 44, 186–215 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  23. Nadarajah, S., Kotz, S.: The beta exponential distribution. Reliab. Eng. Syst. Saf. 91, 689–697 (2006)

    Article  MATH  Google Scholar 

  24. Nadarajah, S., Rocha, R.: Newdistns: an R package for new families of distributions. J. Stat. Softw. 69(10), 1–32 (2016)

    Article  Google Scholar 

  25. Nichols, M.D., Padgett, W.J.: A bootstrap control chart for Weibull percentiles. Qual. Reliab. Eng. Int. 22, 141–151 (2006)

    Article  Google Scholar 

  26. Olapade, A.K.: On characterizations of the half logistic distribution. InterStat 2, 1–7 (2003)

    Google Scholar 

  27. Olapade, A.K.: The type I generalized half logistic distribution. J. Iran. Stat. Soc. 13(1), 69–82 (2014)

    MathSciNet  MATH  Google Scholar 

  28. Oliveira, J., Santos, J., Xavier, C., Trindade, D., Cordeiro, G.M.: The McDonald half-logistic distribution: theory and practice. Commun. Stat. Theory Methods 45(7), 2005–2022 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  29. Parzen, E.: Nonparametric statistical modelling (with comments). J. Amer. Statist. Assoc. 74, 105–131 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  30. R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2009)

  31. Rayner, J.C.W., Best, D.J.: Smooth Tests of Goodness of Fit. Oxford University Press, Oxford (1989)

    MATH  Google Scholar 

  32. Scott, D.W., Gotto, A.M., Cole, J.S., Gory, G.A.: Plasma lipids as collateral risk factors in coronory artery disease: a case study of male with chest pain. J. Coronory Dis. 31(2), 337–345 (1978)

    Article  Google Scholar 

  33. Shaked, M., Shanthikumar, J.G.: Stochastic Orders and their Applications. Academic Press, New York (1994)

    MATH  Google Scholar 

  34. Smith, R.L., Naylor, J.C.: A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. J. R. Stat. Soc. Ser. C 36, 358–369 (1987)

    MathSciNet  Google Scholar 

  35. Torabi, H., Bagheri, F.L.: Estimation of parameters for an extended generalized half logistic distribution based on complete and censored data. JIRSS 9(2), 171–195 (2010)

    MathSciNet  MATH  Google Scholar 

  36. Yegen, D., Ozel, G.: Marshall-Olkin half logistic distribution with theory and applications. Alphanum. J. 6(2), 408–416 (2018)

    Article  Google Scholar 

  37. Zografos, K., Balakrishnan, N.: On families of beta- and generalized gamma-generated distributions and associated inference. Stat. Methodol. 6, 344–362 (2009)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

We would like to express our gratitude to the two reviewers for their detailed remarks on the work.

Author information

Authors and Affiliations

  1. Department of Statistics, Faculty of Computing, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan

    Rana Muhammad Imran Arshad, M. H. Tahir, Sadaf Khan & Farrukh Jamal

  2. Department of Mathematics, LMNO, University of Caen, 14032, Caen, France

    Christophe Chesneau

Authors
  1. Rana Muhammad Imran Arshad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. H. Tahir
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Christophe Chesneau
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sadaf Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Farrukh Jamal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christophe Chesneau.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Communicated by Javier E. Contreras-Reyes.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arshad, R.M.I., Tahir, M.H., Chesneau, C. et al. The gamma power half-logistic distribution: theory and applications. São Paulo J. Math. Sci. 17, 1142–1169 (2023). https://doi.org/10.1007/s40863-022-00331-x

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40863-022-00331-x

Keywords

Mathematics subject classification

Search

Navigation